I want to order the vertices in ascending order (1,2,3,...), i.e. I want vertices with consecutive labels to be adjacent on the circle, like a clock - i.e. as in the image below, which I had to construct by making the connections more or less consecutive:

Mathematica has its own ideas! It insists on ordering the vertices by the order in which it encounters them in the list of connections, (i.e. 1,5,4,3,...) in the above example. Sorting the list of connections doesn't fix this problem. This issue doesn't seem to be well documented. Any suggestions for a workaround?

Could you also elaborate a bit on how your result should look like? I do not get it yet - although others may ;-). If you get another upvote you´ll be able to post images etc. as well.
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Yves KlettSep 18 '12 at 7:52

You can get what you need with Graph easily if GraphPlot is not otherwise essential for your application. Like GraphPlot, Graph takes the list of vertices as they appear in the list of edges if a list of vertices is not provided, but, unlike GraphPlot, it also accepts the list of vertices as an argument.

With a few lines to almost replicate the rendering you get in GraphPlot:

One approach might be to extract the VertexCoordinateRules from an appropiate GraphPlot (for example from {1->2, 2-> 3, 3-> 4 ...}) using Cases, and use these to order the vertices in the graph of interest.

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